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5.3

5.3. Function Rules, Tables, & Graphs. List some pairs of numbers that will satisfy the equation x + y = 4. x = 1 and y = 3 x = 2 and y = 2 x = 4 and y = 0 What about negative numbers? If x = -1 then y = ? y = 5. x + y = 4 What about decimals? If x = 2.6 then y = ?. y = 1.4

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5.3

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  1. 5.3 Function Rules, Tables, & Graphs

  2. List some pairs of numbers that will satisfy the equation x + y = 4. x = 1 and y = 3 x = 2 and y = 2 x = 4 and y = 0 What about negative numbers? If x = -1 then y = ? y = 5

  3. x + y = 4What about decimals?If x = 2.6 then y = ? y = 1.4 Now, let’s graph the pairs of numbers we have listed.

  4. (1, 3) (2, 2) (4, 0) (-1, 5) (2.6, 1.4) Connect the points on your graph. What does the graph look like? • • • • •

  5. It is a straight line! It is a linear relation. • • What does the line represent? All solutions for the equation x+y=4! Is (3, -1) a solution to this equation? NO! You can check by graphing it or plugging into the equation! • • •

  6. 5.3 – Function Rules, Graphs, Tables A function can be written as: 1) Rule: f(x) = 2x + 3

  7. 5.3 – Function Rules, Graphs, Tables A function can be written as: 2) Table

  8. 5.3 – Function Rules, Graphs, Tables A function can be written as: 3) Graph

  9. 5.3 – Function Rules, Graphs, Tables • Continuous Data – Data where the numbers between any two points have value. Connect the points with a smooth (straight) line. Examples: length, weight and distance.

  10. 5.3 – Function Rules, Graphs, Tables • Discrete Data – Data that involves counting whole numbers. Don’t connect the points. Examples: cars, people and dogs.

  11. 5.3 – Function Rules, Graphs, Tables • Graphing functions – be careful when you connect the points in a function. Some require a straight line, some a curved line. y = |x| + 1 y = x + 1

  12. x y=2x+1 y 0 1 4 Answer Now Let’s review tables!Graph y = 2x + 1 using the domain {0, 1, 4} • Make sure the equation is solved for y. • Create a t-table using the domain values. • Plug in the domain values and solve for the range. • Plot the points and connect them to create the line.

  13. Answer Now Let’s review the graphing calculator!Graph y = 2x + 1 • Select TABLE from the Main Menu • Make sure the equation is solved for y. Type in the right side of the equation. • Select TABL (F6) from the options • Type the domain values and press EXE • Select G-CON from the options. This plots the points and connects them to form the line.

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